基于L1范数正则项约束的不连续资料三维/四维变分融合研究

doi:10.11867/j.issn.1001-8166.2017.07.0757

地球科学进展 ›› 2017, Vol. 32 ›› Issue (7): 757 -768. doi: 10.11867/j.issn.1001-8166.2017.07.0757

王根 ^1, ²(

), 盛绍学 ¹, 刘惠兰 ¹, 吴蓉 ³, 杨寅 ⁴

1.安徽省气象信息中心安徽省大气科学与卫星遥感重点实验室, 安徽合肥 230031
2.中国气象局沈阳大气环境研究所, 辽宁沈阳 110000
3.安徽省气候中心, 安徽合肥 230031
4.国家气象中心, 北京 100081

收稿日期:2017-02-26 修回日期:2017-05-30 出版日期:2017-07-20
基金资助:
安徽省自然科学基金项目“广义变分同化AIRS水汽通道亮温及在安徽强对流天气预报中的应用研究”(编号:1708085QD89);淮河流域气象开放研究基金项目“基于地面和卫星观测反演的江淮流域降水资料融合算法研究”(编号:HRM201407)资助

Discontinuous Data 3D/4D Variation Fusion Based on the Constraint of L1 Norm Regularization Term

Gen Wang ^1, ²( ), Shaoxue Sheng ¹, Huilan Liu ¹, Rong Wu ³, Yin Yang ⁴

1.Anhui Meteorological Information Centre Anhui Key Laboratory of Atmospheric Science and Satellite Remote Sensing, Hefei 230031, China
2.The Institute of Atmospheric Environment, China Meteorological Administration, Shenyang 110000, China
3.Anhui Climate Center, Hefei 230031, China
4.National Meteorological Center of China, Beijing 100081, China

Received:2017-02-26 Revised:2017-05-30 Online:2017-07-20 Published:2017-07-20
About author:
First author:Wang Gen(1983-),male,Taizhou City, Jiangsu Province, Engineer. Research areas include satellite data assimilation, numerical simulation of GRAPES and multi-source data fusion.E-mail:203wanggen@163.com
Supported by:
Project supported by the Natural Science Foundation of Anhui Province“Generalised variational assimilation of AIRS water vapor channel brightness temperature and the application study in severe convective weather in Anhui Province”(No.1708085QD89);The Open Research Fund of Huai River Basin in Meteorological “Study of precipitation data fusion algorithm in Jianghuai Basin based on the ground and satellite observations”(No.HRM201407)

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经典三维/四维变分融合基于误差服从高斯分布,在极小化迭代时涉及到求解目标泛函梯度,若资料不连续则不可微,从而无法求解相应梯度,故理论要求所融合的资料必须具有“连续性”。采用扩展经典三维/四维变分融合方法,显式地基于L1范数把先验知识作为正则项约束项耦合到经典变分融合模型。在实施过程中把资料映射到小波域,采用新的融合模型在“小波空间”完成资料融合后,再采用小波逆变换映射回“观测空间”。通过线性平流扩散方程作为四维预报模式进行理想试验,试验设计融合背景和观测资料不连续,即在某些点左右导数不相等,试验结果表明文中采用的方法可行。进一步将该方法用于多源降水资料融合试验,采用基于GAMMA拟合函数的概率密度匹配法(Probability Density Function matching method,PDF)进行CMORPH反演降水资料订正,再将订正后的资料与地面站观测资料进行融合。通过与参考场结构相似性度量,得到该方法能更好地保留代表一些天气现象的“离群点”。该融合方法为不连续资料融合,尤其是“跳变点”的变分融合奠定了理论基础并提供了可借鉴的方法。

关键词: 不连续资料, 变分融合, L1范数, 正则项, 小波空间

Classical 3D/4D variation fusion is based on the theory that error follows Gaussian distribution. When using minimization iteration, the gradient of objective function is involved, and the solution of which requires the continuity of data. This paper adopted the extended classical 3D/4D variation fusion method, and explicitly applied the prior knowledge, which was based on L1-norm, as regularization constraint to the classical variation fusion method. Original data was firstly projected into the wavelet domain during the implementation process, and new fusion model was adopted for data fusion in wavelet space, then inverse wavelet transform was used to project the result to the observation space. Ideal experiment was carried out by using linear advection-diffusion equation as four-dimensional prediction model, which made a hypothesis of the discontinuity with the data between background and observation, and that meant the derivatives between left and right were not equal on some points. The result of the experiment showed that the method adopted here was practicable. A further research was also done for multi-source precipitation fusion. Firstly, CMORPH inversion precipitation data were corrected through PDF (Probability Density Function, PDF) matching method based on GAMMA fitting function. Then corrected data was fused with the observation one. By comparison with the reference field, the result showed that this method can keep some outliers better, which might represent certain weather phenomenon. The L1-norm regularization variation fusion in this paper provided a possible way to deal with discrete data, especially for jump point.

Key words: Discrete data, Variation fusion, L1-norm, Regularization term, Wavelet space.

中图分类号:

P468

图1 构建“真实状态”
(a)分段函数(记为PF);(b)二次函数(记为QF);(c)正弦函数(记为SF);(d)平方指数函数(记为SEF)

Fig.1 Building true state
(a) Piecewise Function (PF); (b) Quadratic Function (QF); (c) Sine Function (SF); (d) Square Exponential Function (SEF)

图2 经典变分融合和耦合L1范数正则化的融合效果对比分析

Fig.2 Fusion effect analysis of classic variational fusion and coupling L1 norm regularization method

表1 经典变分和耦合L1范数正则化融合的MSE _r,MAE _r和BIAS _r对比分析

Table 1 Comparative analysis fusion result of classical variational and coupling L1 norm regularization based on the method of MSE _r, MAE _r and BIAS _r

	MSE_r		MAE_r		BIAS_r
	R4D-Var	4DVar	R4D-Var	4DVar	R4D-Var	4DVar
PF	0.0591	0.0617	0.0613	0.0848	0.0687	0.0637
QF	0.0373	0.0426	0.0322	0.0513	0.0392	0.0363
SF	0.0479	0.0557	0.0437	0.0625	0.0486	0.0450
SEF	0.0251	0.0266	0.0238	0.0353	0.0266	0.0246

表1 经典变分和耦合L1范数正则化融合的MSE _r,MAE _r和BIAS _r对比分析

Table 1 Comparative analysis fusion result of classical variational and coupling L1 norm regularization based on the method of MSE _r, MAE _r and BIAS _r

	MSE_r		MAE_r		BIAS_r
	R4D-Var	4DVar	R4D-Var	4DVar	R4D-Var	4DVar
PF	0.0591	0.0617	0.0613	0.0848	0.0687	0.0637
QF	0.0373	0.0426	0.0322	0.0513	0.0392	0.0363
SF	0.0479	0.0557	0.0437	0.0625	0.0486	0.0450
SEF	0.0251	0.0266	0.0238	0.0353	0.0266	0.0246

图3 代表站累积概率匹配图和安徽国家站偏差分布图
(a)CMORPH和雨量计累积概率匹配;(b)CMORPH降水资料对应的国家站偏差值

Fig.3 Cumulative probability matching of representative station and bias distribution of national station in Anhui Province
(a) Cumulative probability matching of CMORPH and rain gauge; (b) Bias value of CMORPH of corresponding station

图4 不同正则化参数的融合降水场与参考场的降水分布结构对比

Fig.4 Comparison structure of precipitation fusion based on different regularization parameter and reference field

图5 参数不同值融合场与参考场和CMORPH的结构相似性SSIM对比分析

Fig.5 Comparative analysis of SSIM between fusion field based on different value of parameters and reference field and CMORPH

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